Formal Monotony Analysis of~Neural Networks with~Mixed Inputs: An Asset for~Certification

This paper proves monotony property of Neural networks that model a physical system (breaks in an airplane), where monotony is a physical property of the approximated model that we want the NN to have.

Today, state-of-the-art methods for enforcing partial monotony No citation here, what are they refering to? De Maria et al?

They propose a refinement of the monotony property: it has to be monotonous only in the desired area -> moving the burden of verification from the verifier to the specification

Related works discussion: Some methods merely encourage monotony without enforcing it. Some methods enforce it for continuous variables Others use hand-designed structures that enforce monotony but make training harder Urban, C., Christakis, M., W ̈ ustholz, V., Zhang, F.: Perfectly parallel fairness certification of neural networks, considers monotony for discrete input spaces

The goal is not to prove monotonicity glabally but identify regions for which monotonicity holds and those which don’t. Could this be translated to a structural property, i.e. quantified on networks?